Nonasymptotic form of the recursion relations of the three-dimensional Ising model

Approximate recurrence relations (RR) in the three-dimensional Ising model are obtained in the form of rapidly convergent series. The representation of RR in the form of nonasymptotical series is related to rejecting the traditional perturbation theory based on the Gaussian measure density. Using the RR obtained, value of the critical exponent of the correlation length $\nu$ is calculated. It is shown that if higher nongaussian basic measures are used then the difference form of the RR implies independence of the critical exponent $\nu$ of $s$ for $s>2$ ($s$ is the parameter of the layer structure of the phase space). The results obtained make it possible to obtain explicit expressions for thermodynamic functions in the neighbourhood of the phase transition point.